For the packet-oriented transmission of data in telecommunications networks between communications terminals and data computers, it is generally known to use a connection-oriented transmission protocol (for example the TCP=Transport Control Protocol). The connection-oriented transmission protocol sets up a connection between the communications terminal and the data computer, over which connection a multiplicity of supervisory measures are carried out. For example, when the transport control protocol is used, it is checked whether all the data packets which are emitted by the respective data transmitter arrive at the respective data receiver, and whether the sequence of the transmitted data packets at the receiver corresponds to the order with which these packets have been emitted at the transmitter. For this purpose, a multiplicity of confirmation messages (“acknowledgements”) are exchanged during the transmission of data between the communications terminal and the data computer. In particular, in networks with long loop transit times (response times), the need to wait for such confirmation messages leads to a reduction in the data transmission rate, although a high physically available bandwidth may possibly be present. During the connection setup and connection release of the data transmission, signaling messages are also repeatedly transmitted to and fro between the communications terminal and the data computer. For example, when the transport control protocol is used for the connection setup, what is referred to as triple handshaking is carried out, and, when it is used for the connection release, what is referred to as quadruple handshaking is carried out. As a result of this multiplicity of security and supervisory measures, the transmission of data between the communications terminal and the data computer is delayed so that significant waiting times may occur during the packet-oriented data transmission.